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• word disambiguation algorithm (Lesk algorithm)

  - by anyssnordin

  Hii.. Can anybody help me to find an algorithm in Java code to find synonyms of a search word based on the context and I want to implement the algorithm with WordNet database. For example, "I am running a Java program". From the context, I want to find the synonyms for the word "running", but the synonyms must be suitable according to a context.

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• Hopcroft–Karp algorithm in Python

  - by Simon

  I am trying to implement the Hopcroft Karp algorithm in Python using networkx as graph representation. Currently I am as far as this: #Algorithms for bipartite graphs import networkx as nx import collections class HopcroftKarp(object): INFINITY = -1 def __init__(self, G): self.G = G def match(self): self.N1, self.N2 = self.partition() self.pair = {} self.dist = {} self.q = collections.deque() #init for v in self.G: self.pair[v] = None self.dist[v] = HopcroftKarp.INFINITY matching = 0 while self.bfs(): for v in self.N1: if self.pair[v] and self.dfs(v): matching = matching + 1 return matching def dfs(self, v): if v != None: for u in self.G.neighbors_iter(v): if self.dist[ self.pair[u] ] == self.dist[v] + 1 and self.dfs(self.pair[u]): self.pair[u] = v self.pair[v] = u return True self.dist[v] = HopcroftKarp.INFINITY return False return True def bfs(self): for v in self.N1: if self.pair[v] == None: self.dist[v] = 0 self.q.append(v) else: self.dist[v] = HopcroftKarp.INFINITY self.dist[None] = HopcroftKarp.INFINITY while len(self.q) > 0: v = self.q.pop() if v != None: for u in self.G.neighbors_iter(v): if self.dist[ self.pair[u] ] == HopcroftKarp.INFINITY: self.dist[ self.pair[u] ] = self.dist[v] + 1 self.q.append(self.pair[u]) return self.dist[None] != HopcroftKarp.INFINITY def partition(self): return nx.bipartite_sets(self.G) The algorithm is taken from http://en.wikipedia.org/wiki/Hopcroft%E2%80%93Karp_algorithm However it does not work. I use the following test code G = nx.Graph([ (1,"a"), (1,"c"), (2,"a"), (2,"b"), (3,"a"), (3,"c"), (4,"d"), (4,"e"),(4,"f"),(4,"g"), (5,"b"), (5,"c"), (6,"c"), (6,"d") ]) matching = HopcroftKarp(G).match() print matching Unfortunately this does not work, I end up in an endless loop :(. Can someone spot the error, I am out of ideas and I must admit that I have not yet fully understand the algorithm, so it is mostly an implementation of the pseudo code on wikipedia

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• How to avoid having very large objects with Domain Driven Design

  - by Pablojim

  We are following Domain Driven Design for the implementation of a large website. However by putting the behaviour on the domain objects we are ending up with some very large classes. For example on our WebsiteUser object, we have many many methods - e.g. dealing with passwords, order history, refunds, customer segmentation. All of these methods are directly related to the user. Many of these methods delegate internally to other child object but this still results in some very large classes. I'm keen to avoid exposing lots of child objects e.g. user.getOrderHistory().getLatestOrder(). What other strategies can be used to avoid this problems?

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• Subclassing to avoid line length

  - by Super User

  The standard line length of code is 80 characters per line. This is accepted and followed by the most of programmers. I working on a state machine of a character and is necessary for me follow this too. I have four classes who pass this limit. I can subclass each class in two more and then avoid the line length limit. class Stand class Walk class Punch class Crouch The new classes would be StandLeft, StandRight and so on. Stand, Walk, Punch and Crouch would be then abstract classes. The question if there is a limit for the long of the hierarchies tree or this is depends of the case.

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• Why should ViewModel route actions to Controller when using the MVCVM pattern?

  - by Lea Hayes

  When reading examples across the Internet (including the MSDN reference) I have found that code examples are all doing the following type of thing: public class FooViewModel : BaseViewModel { public FooViewModel(FooController controller) { Controller = controller; } protected FooController Controller { get; private set; } public void PerformSuperAction() { // This just routes action to controller... Controller.SuperAction(); } ... } and then for the view: public class FooView : BaseView { ... private void OnSuperButtonClicked() { ViewModel.PerformSuperAction(); } } Why do we not just do the following? public class FooView : BaseView { ... private void OnSuperButtonClicked() { ViewModel.Controller.SuperAction(); // or, even just use a shortcut property: Controller.SuperAction(); } }

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• How do I handle priority and propagation in an event system?

  - by Peeter

  Lets say I have a simple event system with the following syntax: object = new Object(); object.bind("my_trigger", function() { print "hello"; }); object.bind("my_trigger", function() { print "hello2"; }); object.trigger("my_trigger"); How could I make sure hello2 is printed out first (I do not want my code to depend on which order the events are binded). Ontop of that, how would I prevent my events from propagating (e.g. I want to stop every other event from being executed)

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• DDD: service contains two repository

  - by tikhop

  Does it correct way to have two repository inside one service and will it be an application or domain service? Suppose I have a Passenger object that should contains Passport (government id) object. I am getting Passenger from PassengerRepository. PassengerRepository create request to server and obtain data (json) than parse received data and store inside repository. I have confused because I want to store Passport as Entity and put it to PassportRepository but all information about password contains inside json than i received above. I guess that I should create a PassengerService that will be include PassengerRepository and PassportRepository with several methods like removePassport, addPassport, getAllPassenger and etc. UPDATE: So I guess that the better way is represent Passport as VO and store all passports inside Passenger aggregate. However there is another question: Where I should put the methods (methods calls server api) for management passenger's passport. I think the better place is so within Passenger aggregate.

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• Space partitioning algorithm

  - by Karol Kolenda

  I have a set of points which are contained within the rectangle. I'd like to split the rectangles into subrectangles based on point density (giving a number of subrectangles or desired density, whichever is easiest). The partitioning doesn't have to be exact (almost any approximation better than regular grid would do), but the algorithm have to cope with the large number of points - approx. 200 millions. The desired number of subrectangles however is substantially lower (around 1000). Does anyone knows any algorithm which may help me with this particular task?

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• Polygonal Triangulation - algorithm with O(n log n) complexity

  - by Arthur Wulf White

  I wish to triangulate a polygon I only have the outline of (p0, p1, p2 ... pn) like described in this question: polygon triangulation algorithm and this webpage: http://cgm.cs.mcgill.ca/~godfried/teaching/cg-projects/97/Ian/algorithm2.html I do not wish to learn the subject and have a deep understanding of it at the moment. I only want to see an effective algorithm that can be used out of the box. The one described in the site seems to be of somewhat high complexity O(n) for finding one ear. I heard this could be done in O(n log n) time. Is there any well known easy to use algorithm that I can translate port to use in my engine that runs with somewhat reasonable complexity? The reason I need to triangulate is that I wish to feel out a 2d-outline and render it 3d. Much like we fill out a 2d-outline in paint. I could use sprites. This would not serve cause I am planning to play with the resulting model on the z-axis, giving it different heights in the different areas. I would love to try the books that were mentioned, although I suspect that is not the answer most readers are hoping for when they read this Q & A format. Mostly I like to see a code snippet I can cut and paste with some modifications and start running.

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• My proposed design is usually worse than my colleague's - how do I get better?

  - by user151193

  I have been programming for couple of years and am generally good when it comes to fixing problems and creating small-to-medium scripts, however, I'm generally not good at designing large scale programs in object oriented way. Few questions Recently, a colleague who has same number of years of experience as me and I were working on a problem. I was working on a problem longer than him, however, he came up with a better solution and in the end we're going to use his design. This really affected me. I admit his design is better, but I wanted to come up with a design as good as his. I'm even contemplating quitting the job. Not sure why but suddenly I feel under some pressure e.g. what would juniors think of me and etc? Is it normal? Or I'm thinking a little too much into this? My job involves programming in Python. I try to read source code but how do you think I can improve me design skills? Are there any good books or software that I should study? Please enlighten me. I will really appreciate your help.

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• A PHP design pattern for the model part [PHP Zend Framework]

  - by Matthieu

  I have a PHP MVC application using Zend Framework. As presented in the quickstart, I use 3 layers for the model part : Model (business logic) Data mapper Table data gateway (or data access object, i.e. one class per SQL table) The model is UML designed and totally independent of the DB. My problem is : I can't have multiple instances of the same "instance/record". For example : if I get, for example, the user "Chuck Norris" with id=5, this will create a new model instance wich members will be filled by the data mapper (the data mapper query the table data gateway that query the DB). Then, if I change the name to "Duck Norras", don't save it in DB right away, and re-load the same user in another variable, I have "synchronisation" problems... (different instances for the same "record") Right now, I use the Multiton pattern : like Singleton, but multiple instances indexed by a key (wich is the user ID in our example). But this is complicating my developpement a lot, and my testings too. How to do it right ?

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• Interface Design Problem: Storing Result of Transactions

  - by jboyd

  Requirements: multiple sources of input (social media content) into a system multiple destinations of output (social media api's) sources and destinations WILL be added some pseudo: IContentProvider contentProvider = context.getBean("contentProvider"); List<Content> toPost = contentProvider.getContent(); for (Content c : toPost) { SocialMediaPresence smPresence = socialMediaService.getSMPresenceBySomeId(c.getDestId()); smPresence.hasTwitter(); smPresence.hasFacebook(); //just to show what this is smPresence.postContent(c); //post content could fail for some SM platforms, but shoulnd't be lost forever } So now I run out of steam, I need to know what content has been successfully posted, and if it hasn't gone too all platforms, or if another platform were added in the future that content needs to go out for it as well (therefore my content provider will need to not only know if content has gone out, but for what platforms). I'm not looking for code, although sample/pseudo is fine... I'm looking for an approach to this problem that I can implement

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• Expose subset of a class - design question

  - by thanikkal

  Suppose i have a product class with about close to 100 properties. Now for some operations (Say tax calculation) i dont really need this bulky product type, rather only a subset that has price related properties. I am not sure if i should create different snap shots(class) of products that just has the properties that i am interested in. what would be the ideal approach so that i don't unnecessarily pass around unsought fluff? Thanks in advance.

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• Choosing a design pattern for a class that might change it's internal attributes

  - by the_drow

  I have a class that holds arbitrary state and it's defined like this: class AbstractFoo { }; template <class StatePolicy> class Foo : public StatePolicy, public AbstractFoo { }; The state policy contains only protected attributes that represent the state. The state might be the same for multiple behaviors and they can be replaced at runtime. All Foo objects have the same interface to abstract the state itself and to enable storing Foo objects in containers. I would like to find the least verbose and the most maintainable way to express this.

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• Non-perfect maze generation algorithm

  - by Shylux

  I want to generate a maze with the following properties: The maze is non-perfect. Means it has loops and multiple ways to reach the exit. The maze should be random. The algorithm should output different mazes for different input parameters The maze doesn't have to be braided. Means dead-ends are allowed and appreciated. I just can't find the right resources on google. The closest i found was this description of the different types of algorithms: http://www.astrolog.org/labyrnth/algrithm.htm. All other algorithms were for perfect mazes. Can anyone give me a website where i can look this up or maybe an algorithm directly?

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• Quick 2D sight area calculation algorithm?

  - by Rogach

  I have a matrix of tiles, on some of that tiles there are objects. I want to calculate which tiles are visible to player, and which are not, and I need to do it quite efficiently (so it would compute fast enough even when I have a big matrices (100x100) and lots of objects). I tried to do it with Besenham's algorithm, but it was slow. Also, it gave me some errors: ----XXX- ----X**- ----XXX- -@------ -@------ -@------ ----XXX- ----X**- ----XXX- (raw version) (Besenham) (correct, since tunnel walls are still visible at distance) (@ is the player, X is obstacle, * is invisible, - is visible) I'm sure this can be done - after all, we have NetHack, Zangband, and they all dealt with this problem somehow :) What algorithm can you recommend for this? EDIT: Definition of visible (in my opinion): tile is visible when at least a part (e.g. corner) of the tile can be connected to center of player tile with a straight line which does not intersect any of obstacles.

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• Book Review: Pro SQL Server 2008 Relational Database Design and Implementation

  - by Alexander Kuznetsov

  Investing in proper database design is a very efficient way to cut maintenance costs. If we expect a system to last, we need to make sure it has a good solid foundation - high quality database design. Surely we can and sometimes do cut corners and save on database design to get things done faster. Unfortunately, such cutting corners frequently comes back and bites us: we may end up spending a lot of time solving issues caused by poor design. So, solid understanding of relational database design is...(read more)

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• Are there any GUI or user interface design patterns? [closed]

  - by Niranjan Kala

  I was curious about GUI design patterns, so I searched and got some information, including a list of UI patterns for the web. This UI patterns website says that: UI Patterns is a growing collection of User Interface Design Principles and User Interface Usability Patterns present on web applications and sites today. Are there any other design patterns for constructing websites or other user interfaces? Are there any books that describe these patterns? I'm particularly interested in patterns for Windows desktop development and web development in the .NET platform.

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• Is there a definitive reference on Pinball playfield design?

  - by World Engineer

  I'm looking at designing tables for Future Pinball but I'm not sure where to start as I've little background in game design per se. I've played scores of pinball tables over the years so I've a fairly good idea of what is "fun" in those terms. However, I'd like to know if there is a definitive "bible" of pinball design as far as layout and scoring/mode design goes. I've looked but there doesn't seem to be anything really coherent that I could find. Is it simply a lost art or am I missing some buried gem?

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• Dijkstra's Bankers Algorithm

  - by idea_

  Could somebody please provide a step-through approach to solving the following problem using the Banker's Algorithm? How do I determine whether a "safe-state" exists? What is meant when a process can "run to completion"? In this example, I have four processes and 10 instances of the same resource. Resources Allocated | Resources Needed Process A 1 6 Process B 1 5 Process C 2 4 Process D 4 7

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• Suggested GA operators for a TSP problem?

  - by Mark

  I'm building a genetic algorithm to tackle the traveling salesman problem. Unfortunately, I hit peaks that can sustain for over a thousand generations before mutating out of them and getting better results. What crossover and mutation operators generally do well in this case?

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• Infinite loop during A* algorithm

  - by Tashu

  The A* algorithm is used by enemies to have a path to the goal. It's working but when sometimes I placed a tower in a grid (randomly) it produces a stack overflow error. The A* algorithm would iterate the enemy and find its path and pass the list to the enemy's path. I added debug logs and the list that I'm getting it looks like it would arrive from start cell to goal cell. Here's the log - 06-19 19:26:41.982: DEBUG/findEnemyPath, enemy X:Y(4281): X2.8256836:Y3.5 06-19 19:26:41.990: DEBUG/findEnemyPath, grid X:Y(4281): X3:Y2 06-19 19:26:41.990: DEBUG/START CELL ID:(4281): 38 06-19 19:26:41.990: DEBUG/GOAL CELL ID:(4281): 47 06-19 19:26:41.990: DEBUG/Best : 38(4281): passThrough:0.0 06-19 19:26:41.990: DEBUG/Neighbor's Parent:(4281): 38 06-19 19:26:41.990: DEBUG/Neighbor's Parent:(4281): 38 06-19 19:26:41.990: DEBUG/Neighbor's Parent:(4281): 38 06-19 19:26:41.990: DEBUG/Neighbor's Parent:(4281): 38 06-19 19:26:41.990: DEBUG/Best : 39(4281): passThrough:8.875 06-19 19:26:41.990: DEBUG/Neighbor's Parent:(4281): 39 06-19 19:26:41.990: DEBUG/Neighbor's Parent:(4281): 39 06-19 19:26:41.990: DEBUG/Neighbor's Parent:(4281): 39 06-19 19:26:41.990: DEBUG/Best : 40(4281): passThrough:7.9375 06-19 19:26:41.990: DEBUG/Neighbor's Parent:(4281): 40 06-19 19:26:41.990: DEBUG/Neighbor's Parent:(4281): 40 06-19 19:26:41.990: DEBUG/Best : 52(4281): passThrough:8.9375 06-19 19:26:41.990: DEBUG/Neighbor's Parent:(4281): 52 06-19 19:26:41.990: DEBUG/Neighbor's Parent:(4281): 52 06-19 19:26:41.990: DEBUG/Best : 53(4281): passThrough:7.96875 06-19 19:26:41.990: DEBUG/Neighbor's Parent:(4281): 53 06-19 19:26:41.990: DEBUG/Best : 28(4281): passThrough:8.9375 06-19 19:26:41.990: DEBUG/Neighbor's Parent:(4281): 28 06-19 19:26:41.990: DEBUG/Best : 65(4281): passThrough:8.984375 06-19 19:26:41.990: DEBUG/Neighbor's Parent:(4281): 65 06-19 19:26:41.990: DEBUG/Neighbor's Parent:(4281): 65 06-19 19:26:41.990: DEBUG/Best : 66(4281): passThrough:7.9921875 06-19 19:26:41.990: DEBUG/Neighbor's Parent:(4281): 66 06-19 19:26:42.000: DEBUG/Best : 78(4281): passThrough:8.99609375 06-19 19:26:42.000: DEBUG/Neighbor's Parent:(4281): 78 06-19 19:26:42.000: DEBUG/Best : 79(4281): passThrough:7.998046875 06-19 19:26:42.000: DEBUG/Neighbor's Parent:(4281): 79 06-19 19:26:42.000: DEBUG/Best : 80(4281): passThrough:6.9990234375 06-19 19:26:42.000: DEBUG/Neighbor's Parent:(4281): 80 06-19 19:26:42.000: DEBUG/Neighbor's Parent:(4281): 80 06-19 19:26:42.000: DEBUG/Best : 81(4281): passThrough:5.99951171875 06-19 19:26:42.000: DEBUG/Neighbor's Parent:(4281): 81 06-19 19:26:42.000: DEBUG/Neighbor's Parent:(4281): 81 06-19 19:26:42.000: DEBUG/Best : 82(4281): passThrough:4.999755859375 06-19 19:26:42.000: DEBUG/Neighbor's Parent:(4281): 82 06-19 19:26:42.000: DEBUG/Neighbor's Parent:(4281): 82 06-19 19:26:42.000: DEBUG/Best : 83(4281): passThrough:3.9998779296875 06-19 19:26:42.000: DEBUG/Neighbor's Parent:(4281): 83 06-19 19:26:42.000: DEBUG/Best : 71(4281): passThrough:2.99993896484375 06-19 19:26:42.000: DEBUG/Neighbor's Parent:(4281): 71 06-19 19:26:42.000: DEBUG/Best : 59(4281): passThrough:1.99951171875 06-19 19:26:42.000: DEBUG/Neighbor's Parent:(4281): 59 06-19 19:26:42.000: DEBUG/Neighbor's Parent:(4281): 59 06-19 19:26:42.000: DEBUG/Neighbor's Parent:(4281): 59 06-19 19:26:42.000: DEBUG/Best : 47(4281): passThrough:0.99951171875 Then, the goal cell would be iterating its parent till start cell to break off the loop. private void populateBestList(Cell cell, List<Cell> bestList) { bestList.add(cell); if (cell.parent.start == false) { Log.d("ID:", ""+cell.id); Log.d("ParentID:", ""+cell.parent.id); populateBestList(cell.parent, bestList); } return; } The log with error above would show like this - 06-19 19:26:42.010: DEBUG/ID:(4281): 47 06-19 19:26:42.010: DEBUG/ParentID:(4281): 59 06-19 19:26:42.010: DEBUG/ID:(4281): 59 06-19 19:26:42.010: DEBUG/ParentID:(4281): 71 06-19 19:26:42.010: DEBUG/ID:(4281): 71 06-19 19:26:42.010: DEBUG/ParentID:(4281): 59 06-19 19:26:42.010: DEBUG/ID:(4281): 59 06-19 19:26:42.010: DEBUG/ParentID:(4281): 71 06-19 19:26:42.010: DEBUG/ID:(4281): 71 71 and 59 would switch over and goes on. I thought the grid is the issue due to the fact that enemies are using the single grid so I make the parent, start, and goal clear before starting the A* algorithm for an enemy. for(int i = 0; i < GRID_HEIGHT; i++) { for(int j = 0; j < GRID_WIDTH; j++) { grid[i][j].parent = null; grid[i][j].start = false; grid[i][j].goal = false; } } That didn't work. I thought it might be something related to this code, but not sure if I'm on right track - neighbor.parent = best; openList.remove(neighbor); closedList.remove(neighbor); openList.add(0, neighbor); Here's the code of the A* algorithm - private List<Cell> findEnemyPath(Enemy enemy) { for(int i = 0; i < GRID_HEIGHT; i++) { for(int j = 0; j < GRID_WIDTH; j++) { grid[i][j].parent = null; grid[i][j].start = false; grid[i][j].goal = false; } } List<Cell> openList = new ArrayList<Cell>(); List<Cell> closedList = new ArrayList<Cell>(); List<Cell> bestList = new ArrayList<Cell>(); int width = (int)Math.floor(enemy.position.x); int height = (int)Math.floor(enemy.position.y); width = (width < 0) ? 0 : width; height = (height < 0) ? 0 : height; Log.d("findEnemyPath, enemy X:Y", "X"+enemy.position.x+":"+"Y"+enemy.position.y); Log.d("findEnemyPath, grid X:Y", "X"+height+":"+"Y"+width); Cell start = grid[height][width]; Cell goal = grid[ENEMY_GOAL_HEIGHT][ENEMY_GOAL_WIDTH]; if(start.id != goal.id) { Log.d("START CELL ID: ", ""+start.id); Log.d("GOAL CELL ID: ", ""+goal.id); //Log.d("findEnemyPath, grid X:Y", "X"+start.position.x+":"+"Y"+start.position.y); start.start = true; goal.goal = true; openList.add(start); while(openList.size() > 0) { Cell best = findBestPassThrough(openList, goal); //Log.d("ID:", ""+best.id); openList.remove(best); closedList.add(best); if (best.goal) { System.out.println("Found Goal"); System.out.println(bestList.size()); populateBestList(goal, bestList); /* for(Cell cell : bestList) { Log.d("ID:", ""+cell.id); Log.d("ParentID:", ""+cell.parent.id); } */ Collections.reverse(bestList); Cell exit = new Cell(13.5f, 3.5f, 1, 1); exit.isExit = true; bestList.add(exit); //Log.d("PathList", "Enemy ID : " + enemy.id); return bestList; } else { List<Cell> neighbors = getNeighbors(best); for (Cell neighbor : neighbors) { if(neighbor.isTower) { continue; } if (openList.contains(neighbor)) { Cell tmpCell = new Cell(neighbor.position.x, neighbor.position.y, 1, 1); tmpCell.parent = best; if (tmpCell.getPassThrough(goal) >= neighbor.getPassThrough(goal)) { continue; } } if (closedList.contains(neighbor)) { Cell tmpCell = new Cell(neighbor.position.x, neighbor.position.y, 1, 1); tmpCell.parent = best; if (tmpCell.getPassThrough(goal) >= neighbor.getPassThrough(goal)) { continue; } } Log.d("Neighbor's Parent: ", ""+best.id); neighbor.parent = best; openList.remove(neighbor); closedList.remove(neighbor); openList.add(0, neighbor); } } } } Log.d("Cannot find a path", ""); return null; }

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• Disk Search / Sort Algorithm

  - by AlgoMan

  Given a Range of numbers say 1 to 10,000, Input is in random order. Constraint: At any point only 1000 numbers can be loaded to memory. Assumption: Assuming unique numbers. I propose the following efficient , "When-Required-sort Algorithm". We write the numbers into files which are designated to hold particular range of numbers. For example, File1 will have 0 - 999 , File2 will have 1000 - 1999 and so on in random order. If a particular number which is say "2535" is being searched for then we know that the number is in the file3 (Binary search over range to find the file). Then file3 is loaded to memory and sorted using say Quick sort (which is optimized to add insertion sort when the array size is small ) and then we search the number in this sorted array using Binary search. And when search is done we write back the sorted file. So in long run all the numbers will be sorted. Please comment on this proposal.

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• Help with Algorithm chinese auction

  - by sam munkes

  Hi, i am designing a Chinese auction website. Tickets ($5, $10 & $20) are sold either individually, or via packages to receive discounts. There are various Ticket packages for example: 5-$5 tickets = receive 10% off 5-$10 tickets = receive 10% off 5-$20 tickets = receive 10% off 5-$5 tickets + 5-$10 tickets + 5-$20 tickets = receive 15% off When users add tickets to their cart, i need to figure out the cheapest package(s) to give them. the trick is that if a user adds 4-$5 tickets + 5-$10 tickets + 5-$20 tickets, it should still give him package #3 since that would be the cheapest for him. Any help in figuring out a algorithm to solve this, or any tips would be greatly appreciate it. thanks

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• Algorithm to price bulk discounts

  - by sam munkes

  Hi, i am designing a Chinese auction website. Tickets ($5, $10 & $20) are sold either individually, or via packages to receive discounts. There are various Ticket packages for example: 5-$5 tickets = receive 10% off 5-$10 tickets = receive 10% off 5-$20 tickets = receive 10% off 5-$5 tickets + 5-$10 tickets + 5-$20 tickets = receive 15% off When users add tickets to their cart, i need to figure out the cheapest package(s) to give them. the trick is that if a user adds 4-$5 tickets + 5-$10 tickets + 5-$20 tickets, it should still give him package #4 since that would be the cheapest for him. Any help in figuring out a algorithm to solve this, or any tips would be greatly appreciate it. thanks

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